POINT #1: Most people believe we have a Democracy style of government and that is precisely the problem with your statement.
The United States was set up as a Republic style of government. Article IV Section 4, of the Constitution "guarantees to every state in this union a Republican form of government".... Conversely, the word Democracy is not mentioned even once in the Constitution.
POINT #2: I said it was the oldest current government, not the oldest style. Perhaps I should clarify my statement. Every country (as far as I am aware of) has had their government formed since the United States of America was formed and enacted our government under the constitution that we still abide by.
If you are aware of an older government I'm all ears.